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SageMath
E = EllipticCurve("dm1")
E.isogeny_class()
Elliptic curves in class 485520dm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485520.dm2 | 485520dm1 | \([0, -1, 0, -4154760, 30475407600]\) | \(-16329068153/816480000\) | \(-396593682031700213760000\) | \([2]\) | \(60162048\) | \(3.2081\) | \(\Gamma_0(N)\)-optimal* |
485520.dm1 | 485520dm2 | \([0, -1, 0, -173948040, 877811792112]\) | \(1198345620520313/8268750000\) | \(4016429071501593600000000\) | \([2]\) | \(120324096\) | \(3.5546\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 485520dm have rank \(0\).
Complex multiplication
The elliptic curves in class 485520dm do not have complex multiplication.Modular form 485520.2.a.dm
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.